"Oh, of course no one ever really *does* it..." A compressed version of my own confusion as a maths student: https://personalpages.manchester.ac.uk/staff/hung.bui/ideal.pdf …pic.twitter.com/ooasn01bfe
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Yeah, I'd say the main differences are a) maths had a massive crisis in foundations in the early 20th c, so weird stuff happens in the 'machine code' layer anyway...
... and more importantly b) proofs mathematicians write are *not* just written in a higher-order language that can be mapped cleanly onto lower-level primitives, they use all kinds of messy human language to explain things.
